To investigate temperature-dependent optical properties of PLCCO, we measured the \(ab\)  plane reflectance of each sample across a wide spectral range from 75 to 35000 cm\(^{-1}\)  at various selected temperatures ranging from 8 to 300 K (see Supplementary Information). For the reflectance measurements, the incident angle was near normal (\(\sim \) 11\(^{\circ }\) ). To cover the wide spectral range, a Fourier-transform infrared (FTIR)-type spectrometer (Bruker Vertex 80v: 75 – 8000 cm\(^{-1}\) ) and a monochromatic spectrometer (Perkin-Elmer Lambda 950: 5000 – 35000 cm\(^{-1}\) ) were used. For the temperature-dependent study, a continuous flow liquid He cryostat was used. An in-situ metallization method [1]} was employed to obtain accurate reflectance spectra. We checked how accurately the samples were cut and polished along the \(ab\)  plane with a simple experiment using a polarizer and confirmed that miscut effects in the measured reflectance spectra were negligibly small (see Supplementary Information). The optical conductivity was obtained from the measured reflectance spectrum by using the Kramers–Kronig (KK) relation, Fresnel formula, and relations between optical constants [2]}, [3]}. To perform the KK analysis, one has to extrapolate the measured reflectance spectrum in a finite spectral range to both zero and infinity frequencies. For the extrapolation from the lowest data point to zero frequency, the Hagen–Rubens relation (i.e., \(1 - R(\omega ) \propto \sqrt{\omega }\) ) and \(1 - R(\omega ) \propto \omega ^4\)  were used for the normal and superconducting states, respectively. For the extrapolation from the highest data point (35,000 cm\(^{-1}\) ) to the infinity, it was assumed that \(R(\omega ) \propto 1/\omega \)  up to 1.0\(\times \) 10\(^6\)  cm\(^{-1}\)  and the reflectance follows the free electron behavior[2]}, [3]} (i.e., \(R(\omega ) \propto 1/\omega ^4\) ) above 1.0\(\times \) 10\(^6\)  cm\(^{-1}\) .
